A Learner-Refiner Framework for Barrier Certificate Generation
Year: 2025
Type: article
Abstract: Barrier certificate is a powerful tool for verifying they safety property of dynamical systems. In this paper, we introduce an innovative learner–refiner framework for synthesizing polynomial barrier certificates. The framework comprises a learner and a refiner, which work inductively to generate barrier certificates. More specifically, the learner trains barrier certificate candidates represented by feedforward neural networks with polynomial activations, while the refiner utilizes sums of squares (SOS) programming to either validate the candidates or recover valid barrier certificates. Our framework achieves great efficiency via supervised learning, and it ensures formal soundness using SOS-based verification. We implement the LR4BC tool, and we perform a comprehensive experimental evaluation using several benchmarks. The results demonstrate that our tool not only successfully synthesizes polynomial barrier certificates undetected via the SOS-based tool PRoTECT but also achieves a significant speedup in efficiency compared to the neural network-based tool FOSSIL 2.0.
Source: Mathematics
DOI: 10.3390/math13050848
Authors: Deng Chen, Wang Lin, Zuohua Ding
Institution: Zhejiang Sci-Tech University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
Award: G400648788
OpenAlex ID: W4408155622